In [1]:
import dask.dataframe as dd
import pandas as pd
import folium
import datetime
import time
import numpy as np
import matplotlib
matplotlib.use('nbagg')
import matplotlib.pylab as plt
import seaborn as sns
from matplotlib import rcParams
import gpxpy.geo
from sklearn.cluster import MiniBatchKMeans, KMeans#Clustering
import math
import pickle
import os
import xgboost as xgb
from sklearn.ensemble import RandomForestRegressor
from sklearn.metrics import mean_squared_error
from sklearn.metrics import mean_absolute_error
import warnings
warnings.filterwarnings("ignore")
Data Information¶
Ge the data from : http://www.nyc.gov/html/tlc/html/about/trip_record_data.shtml (2016 data) The data used in the attached datasets were collected and provided to the NYC Taxi and Limousine Commission (TLC)
Information on taxis:¶
Yellow Taxi: Yellow Medallion Taxicabs
These are the famous NYC yellow taxis that provide transportation exclusively through street-hails. The number of taxicabs is limited by a finite number of medallions issued by the TLC. You access this mode of transportation by standing in the street and hailing an available taxi with your hand. The pickups are not pre-arranged.
For Hire Vehicles (FHVs)
FHV transportation is accessed by a pre-arrangement with a dispatcher or limo company. These FHVs are not permitted to pick up passengers via street hails, as those rides are not considered pre-arranged.
Green Taxi: Street Hail Livery (SHL)
The SHL program will allow livery vehicle owners to license and outfit their vehicles with green borough taxi branding, meters, credit card machines, and ultimately the right to accept street hails in addition to pre-arranged rides.
Credits: Quora
Footnote:
In the given notebook we are considering only the yellow taxis for the time period between Jan - Mar 2015 & Jan - Mar 2016Data Collection¶
We Have collected all yellow taxi trips data from jan-2015 to dec-2016(Will be using only 2015 data)
| file name | file name size | number of records | number of features |
|---|---|---|---|
| yellow_tripdata_2016-01 | 1. 59G | 10906858 | 19 |
| yellow_tripdata_2016-02 | 1. 66G | 11382049 | 19 |
| yellow_tripdata_2016-03 | 1. 78G | 12210952 | 19 |
| yellow_tripdata_2016-04 | 1. 74G | 11934338 | 19 |
| yellow_tripdata_2016-05 | 1. 73G | 11836853 | 19 |
| yellow_tripdata_2016-06 | 1. 62G | 11135470 | 19 |
| yellow_tripdata_2016-07 | 884Mb | 10294080 | 17 |
| yellow_tripdata_2016-08 | 854Mb | 9942263 | 17 |
| yellow_tripdata_2016-09 | 870Mb | 10116018 | 17 |
| yellow_tripdata_2016-10 | 933Mb | 10854626 | 17 |
| yellow_tripdata_2016-11 | 868Mb | 10102128 | 17 |
| yellow_tripdata_2016-12 | 897Mb | 10449408 | 17 |
| yellow_tripdata_2015-01 | 1.84Gb | 12748986 | 19 |
| yellow_tripdata_2015-02 | 1.81Gb | 12450521 | 19 |
| yellow_tripdata_2015-03 | 1.94Gb | 13351609 | 19 |
| yellow_tripdata_2015-04 | 1.90Gb | 13071789 | 19 |
| yellow_tripdata_2015-05 | 1.91Gb | 13158262 | 19 |
| yellow_tripdata_2015-06 | 1.79Gb | 12324935 | 19 |
| yellow_tripdata_2015-07 | 1.68Gb | 11562783 | 19 |
| yellow_tripdata_2015-08 | 1.62Gb | 11130304 | 19 |
| yellow_tripdata_2015-09 | 1.63Gb | 11225063 | 19 |
| yellow_tripdata_2015-10 | 1.79Gb | 12315488 | 19 |
| yellow_tripdata_2015-11 | 1.65Gb | 11312676 | 19 |
| yellow_tripdata_2015-12 | 1.67Gb | 11460573 | 19 |
In [2]:
# List of features at Jan 2015
month = dd.read_csv('yellow_tripdata_2015-01.csv')
print(month.columns)
In [3]:
# How operation on Dask instead of Pandas
month.visualize()
Out[3]:
In [4]:
month.fare_amount.sum().visualize()
Out[4]:
Features in the dataset:¶
| Field Name | Description |
|---|---|
| VendorID |
A code indicating the TPEP provider that provided the record.
|
| tpep_pickup_datetime | The date and time when the meter was engaged. |
| tpep_dropoff_datetime | The date and time when the meter was disengaged. |
| Passenger_count | The number of passengers in the vehicle. This is a driver-entered value. |
| Trip_distance | The elapsed trip distance in miles reported by the taximeter. |
| Pickup_longitude | Longitude where the meter was engaged. |
| Pickup_latitude | Latitude where the meter was engaged. |
| RateCodeID | The final rate code in effect at the end of the trip.
|
| Store_and_fwd_flag | This flag indicates whether the trip record was held in vehicle memory before sending to the vendor, |
| Dropoff_longitude | Longitude where the meter was disengaged. |
| Dropoff_ latitude | Latitude where the meter was disengaged. |
| Payment_type | A numeric code signifying how the passenger paid for the trip.
|
| Fare_amount | The time-and-distance fare calculated by the meter. |
| Extra | Miscellaneous extras and surcharges. Currently, this only includes. the $0.50 and $1 rush hour and overnight charges. |
| MTA_tax | 0.50 MTA tax that is automatically triggered based on the metered rate in use. |
| Improvement_surcharge | 0.30 improvement surcharge assessed trips at the flag drop. the improvement surcharge began being levied in 2015. |
| Tip_amount | Tip amount – This field is automatically populated for credit card tips.Cash tips are not included. |
| Tolls_amount | Total amount of all tolls paid in trip. |
| Total_amount | The total amount charged to passengers. Does not include cash tips. |
ML Problem Formulation¶
Time-series forecasting and Regression
- To find number of pickups, given location cordinates(latitude and longitude) and time, in the query reigion and surrounding regions.
To solve the above we would be using data collected in Jan - Mar 2015 to predict the pickups in Jan - Mar 2016.
Performance metrics¶
- Mean Absolute percentage error.
- Mean Squared error.
Data Cleaning¶
- Univariant Analysis
- Remove Outliers
In [5]:
month.head(5)
Out[5]:
1. Pickup Latitude and Pickup Longitude¶
It is inferred from the source https://www.flickr.com/places/info/2459115 that New York is bounded by the
- location cordinates(lat,long) - (40.5774, -74.15) & (40.9176,-73.7004)
so hence any cordinates not within these cordinates are not considered by us as we are only concerned with pickups which originate within New York.
In [6]:
# Region that are out of bound
outlier_locations = month[((month.pickup_longitude <= -74.15) | (month.pickup_latitude <= 40.5774)| \
(month.pickup_longitude >= -73.7004) | (month.pickup_latitude >= 40.9176))]
In [9]:
# Map with given range
map_osm = folium.Map(location=[40.734695, -73.990372], tiles='Stamen Toner')
# Taking 10k data as outlier to see the result in map to get better vizualization and understanding
sample_locations = outlier_locations.head(10000)
for i,j in sample_locations.iterrows():
if int(j['pickup_latitude']) != 0:
folium.Marker(list((j['pickup_latitude'],j['pickup_longitude']))).add_to(map_osm)
map_osm
Out[9]:
Observation:- As you can see above that there are some points just outside the boundary but there are a few that are in either South america, Mexico or Canada
2. Dropoff Latitude & Dropoff Longitude¶
It is inferred from the source https://www.flickr.com/places/info/2459115 that New York is bounded by
- the location cordinates(lat,long) - (40.5774, -74.15) & (40.9176,-73.7004)
so hence any cordinates not within these cordinates are not considered by us as we are only concerned with dropoffs which are within New York.
In [10]:
# Region that are out of bound
outlier_locations = month[((month.dropoff_longitude <= -74.15) | (month.dropoff_latitude <= 40.5774)| \
(month.dropoff_longitude >= -73.7004) | (month.dropoff_latitude >= 40.9176))]
In [11]:
# Map with given range
map_osm = folium.Map(location=[40.734695, -73.990372], tiles='Stamen Toner')
# Taking 10k data as outlier to see the result in map to get better vizualization and understanding
sample_locations = outlier_locations.head(10000)
for i,j in sample_locations.iterrows():
if int(j['pickup_latitude']) != 0:
folium.Marker(list((j['dropoff_latitude'],j['dropoff_longitude']))).add_to(map_osm)
map_osm
Out[11]:
Observation:- The observations here are similar to those obtained while analysing pickup latitude and longitude
3. Trip Durations¶
According to NYC Taxi & Limousine Commision Regulations the maximum allowed trip duration in a 24 hour interval is 12 hours.
In [12]:
month.head()
Out[12]:
In [13]:
# Convert Time into Unix Timestamp
def convert_time_to_unix(s):
'''
To convert time into unix timestamp
'''
return time.mktime(datetime.datetime.strptime(s, "%Y-%m-%d %H:%M:%S").timetuple())
In [17]:
def return_with_trip_times(month):
'''
Calculate Trip duration
Return with features:
Passanger counts, Trip distance, pickup long. and lat., dropoff long. and lat., Total amount, Trip time(duration),
Pickup time, Speed
'''
print('Dask Compute')
duration = month[['tpep_pickup_datetime','tpep_dropoff_datetime']].compute()
# Pickups and Dropoffs datetime to unix timesta,p
duration_pickup = [convert_time_to_unix(x) for x in duration['tpep_pickup_datetime'].values]
duration_drop = [convert_time_to_unix(x) for x in duration['tpep_dropoff_datetime'].values]
# Calculate duration of trips = (Duration dropoff in seconds - Duration pickup in seconds)
# Since it is in seconds, To convert into minutes = divide by 60
durations = (np.array(duration_drop) - np.array(duration_pickup))/float(60)
# Append durations of trips and speed in miles/hr to a new dataframe
print('Appending Features')
new_frame = month[['passenger_count','trip_distance','pickup_longitude','pickup_latitude','dropoff_longitude','dropoff_latitude','total_amount']].compute()
new_frame['trip_times'] = durations
new_frame['pickup_times'] = duration_pickup
# Speed = Distance/Time
# Since Time is in seconds, to convert into mins, replace Time with Time/60
new_frame['Speed'] = 60*(new_frame['trip_distance']/new_frame['trip_times'])
return new_frame
In [18]:
frame_with_durations = return_with_trip_times(month)
In [19]:
# Let see the boxplot of Trip duration
sns.boxplot(y="trip_times", data =frame_with_durations)
plt.show()
In [20]:
# Calculate percentile of trip duration to order to get inferential and perform removal outlier
for i in range(0,100,10):
var = frame_with_durations["trip_times"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(i,var[int(len(var)*(float(i)/100))]))
print ("100 percentile value is ",var[-1])
In [21]:
#looking further from the 99th percecntile
for i in range(90,100):
var = frame_with_durations["trip_times"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(i,var[int(len(var)*(float(i)/100))]))
print ("100 percentile value is ",var[-1])
In [22]:
#removing data based on our analysis and TLC regulations
# Trip duration -- greater than 1 minutes and less than 12hrs(720 minutes)
frame_with_durations_modified=frame_with_durations[(frame_with_durations.trip_times>1) & (frame_with_durations.trip_times<720)]
In [23]:
# Let see box-plot after removal of outliers
sns.boxplot(y="trip_times", data =frame_with_durations_modified)
plt.show()
In [24]:
# Pdf of trip duration after removing the outliers
sns.FacetGrid(frame_with_durations_modified,size=6) \
.map(sns.kdeplot,"trip_times") \
.add_legend();
plt.show()
In [25]:
# Converting the values to log-values to check for log-normal
import math
frame_with_durations_modified['log_times']=[math.log(i) for i in frame_with_durations_modified['trip_times'].values]
In [26]:
# Pdf of log-time
sns.FacetGrid(frame_with_durations_modified,size=6) \
.map(sns.kdeplot,"log_times") \
.add_legend();
plt.show()
In [27]:
# Q-Q plot for checking if trip-times is log-normal
import scipy
scipy.stats.probplot(frame_with_durations_modified['log_times'].values, plot=plt)
plt.show()
4. Speed¶
In [28]:
# Since we removed some of the trip duration time, so this will also affect on speed also
# So, we calculate speed = Distance/Time
# Replace Time with Time/60 (for hrs)
# Remember- Trip duration in previous ones was in minutes and if we divide by 60, then it will coonvert to hrs
# Let see the boxplot of this speed attribute
frame_with_durations_modified['Speed'] = 60*(frame_with_durations_modified['trip_distance']/frame_with_durations_modified['trip_times'])
sns.boxplot(y="Speed", data = frame_with_durations_modified)
plt.show()
In [29]:
# Calculate percentile of speed to order to get inferential and perform removal outlier
for i in range(0,100,10):
var = frame_with_durations_modified["Speed"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(i,var[int(len(var)*(float(i)/100))]))
print("100 percentile value is ",var[-1])
In [30]:
# Calculating speed values on 90th-100th percetile
for i in range(90,100):
var = frame_with_durations_modified["Speed"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(i,var[int(len(var)*(float(i)/100))]))
print("100 percentile value is ",var[-1])
In [31]:
#calculating speed values in 99.0 to 100.0 percentile with interval 0.1
for i in np.arange(0.0, 1.0, 0.1):
var = frame_with_durations_modified["Speed"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(99+i,var[int(len(var)*(float(99+i)/100))]))
print("100 percentile value is ",var[-1])
In [32]:
# Removing further outliers based on the 99.9th percentile value
# Speed -- greater than 0 and less than 45.31
frame_with_durations_modified=frame_with_durations[(frame_with_durations.Speed>0) & (frame_with_durations.Speed<45.31)]
In [33]:
# Avg.speed of cabs in New-York
sum(frame_with_durations_modified["Speed"]) / float(len(frame_with_durations_modified["Speed"]))
Out[33]:
The avg speed in Newyork speed is 12.45miles/hr, so a cab driver can travel 2 miles per 10min on avg.
5. Trip Distance¶
In [34]:
# Upto now we have removed the outliers based on trip durations and speeds
# lets try if there are any outliers in trip distances
# Let see the box-plot in trip-distance
sns.boxplot(y="trip_distance", data =frame_with_durations_modified)
plt.show()
In [35]:
# Calculating trip distance values on percentile with interval 10
for i in range(0,100,10):
var =frame_with_durations_modified["trip_distance"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(i,var[int(len(var)*(float(i)/100))]))
print("100 percentile value is ",var[-1])
In [36]:
# Calculating trip distance values on percentile 90th-100th with interval 1
for i in range(90,100):
var =frame_with_durations_modified["trip_distance"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(i,var[int(len(var)*(float(i)/100))]))
print("100 percentile value is ",var[-1])
In [37]:
# Calculating trip distance values on percentile 99 to 100 with interval 0.1
for i in np.arange(0.0, 1.0, 0.1):
var =frame_with_durations_modified["trip_distance"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(99+i,var[int(len(var)*(float(99+i)/100))]))
print("100 percentile value is ",var[-1])
In [38]:
# Removing further outliers based on the 99.9th percentile value
# Trip distance -- greater than 0 and less than 23
frame_with_durations_modified = frame_with_durations[(frame_with_durations.trip_distance>0) & (frame_with_durations.trip_distance<23)]
In [39]:
# Let see the box-plot after removal of outliers
sns.boxplot(y="trip_distance", data = frame_with_durations_modified)
plt.show()
6. Total Fare¶
In [40]:
# Upto now we have removed the outliers based on trip durations, cab speeds, and trip distances
# lets try if there are any outliers in based on the total fare
# box-plot on fare
sns.boxplot(y="total_amount", data =frame_with_durations_modified)
plt.show()
In [41]:
#calculating total fare amount values on percentile with interval 10
for i in range(0,100,10):
var = frame_with_durations_modified["total_amount"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(i,var[int(len(var)*(float(i)/100))]))
print("100 percentile value is ",var[-1])
In [42]:
#calculating total fare amount values on 90th-100th percentile with interval 1
for i in range(90,100):
var = frame_with_durations_modified["total_amount"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(i,var[int(len(var)*(float(i)/100))]))
print("100 percentile value is ",var[-1])
In [43]:
#calculating total fare amount values on 99-100th percentile with interval 0.1
for i in np.arange(0.0, 1.0, 0.1):
var = frame_with_durations_modified["total_amount"].values
var = np.sort(var,axis = None)
print("{} percentile value is {}".format(99+i,var[int(len(var)*(float(99+i)/100))]))
print("100 percentile value is ",var[-1])
Observation:- As even the 99.9th percentile value doesnt look like an outlier,as there is not much difference between the 99.8th percentile and 99.9th percentile, we move on to do graphical analyis
In [53]:
# Below plot shows us the fare values(sorted) to find a sharp increase to remove those values as outliers
# Plot total fare excluding last two value
plt.plot(var[:-2])
plt.show()
In [54]:
var
Out[54]:
In [56]:
# A very sharp increase in fare values can be seen
# plotting last three total fare values, and we can observe there is share increase in the values
plt.plot(var[-3:])
plt.show()
In [57]:
# Now looking at values not including the last two points, we again find a drastic increase at around 1000 fare value
# we plot last 50 values excluding last two values
plt.plot(var[-50:-2])
plt.show()
Remove all outliers/erronous points.¶
In [58]:
#removing all outliers based on our univariate analysis above
def remove_outliers(new_frame):
a = new_frame.shape[0]
print ("Number of pickup records = ",a)
temp_frame = new_frame[((new_frame.dropoff_longitude >= -74.15) & (new_frame.dropoff_longitude <= -73.7004) &\
(new_frame.dropoff_latitude >= 40.5774) & (new_frame.dropoff_latitude <= 40.9176)) & \
((new_frame.pickup_longitude >= -74.15) & (new_frame.pickup_latitude >= 40.5774)& \
(new_frame.pickup_longitude <= -73.7004) & (new_frame.pickup_latitude <= 40.9176))]
b = temp_frame.shape[0]
print ("Number of outlier coordinates lying outside NY boundaries:",(a-b))
temp_frame = new_frame[(new_frame.trip_times > 0) & (new_frame.trip_times < 720)]
c = temp_frame.shape[0]
print ("Number of outliers from trip times analysis:",(a-c))
temp_frame = new_frame[(new_frame.trip_distance > 0) & (new_frame.trip_distance < 23)]
d = temp_frame.shape[0]
print ("Number of outliers from trip distance analysis:",(a-d))
temp_frame = new_frame[(new_frame.Speed <= 45.31) & (new_frame.Speed >= 0)]
e = temp_frame.shape[0]
print ("Number of outliers from speed analysis:",(a-e))
temp_frame = new_frame[(new_frame.total_amount <1000) & (new_frame.total_amount >0)]
f = temp_frame.shape[0]
print ("Number of outliers from fare analysis:",(a-f))
new_frame = new_frame[((new_frame.dropoff_longitude >= -74.15) & (new_frame.dropoff_longitude <= -73.7004) &\
(new_frame.dropoff_latitude >= 40.5774) & (new_frame.dropoff_latitude <= 40.9176)) & \
((new_frame.pickup_longitude >= -74.15) & (new_frame.pickup_latitude >= 40.5774)& \
(new_frame.pickup_longitude <= -73.7004) & (new_frame.pickup_latitude <= 40.9176))]
new_frame = new_frame[(new_frame.trip_times > 0) & (new_frame.trip_times < 720)]
new_frame = new_frame[(new_frame.trip_distance > 0) & (new_frame.trip_distance < 23)]
new_frame = new_frame[(new_frame.Speed < 45.31) & (new_frame.Speed > 0)]
new_frame = new_frame[(new_frame.total_amount <1000) & (new_frame.total_amount >0)]
print ("Total outliers removed",a - new_frame.shape[0])
print ("---")
return new_frame
In [59]:
print ("Removing outliers in the month of Jan-2015")
print ("----")
frame_with_durations_outliers_removed = remove_outliers(frame_with_durations)
print("fraction of data points that remain after removing outliers", float(len(frame_with_durations_outliers_removed))/len(frame_with_durations))
In [61]:
# Store the coodirnates of the pickup
coords = frame_with_durations_outliers_removed[['pickup_latitude', 'pickup_longitude']].values
neighbours = []
# Define Cluster using KMean algorithm
def find_clusters(increment):
'''
Fit and Predict the cluster using KMean Cluster Algorithm
Return:
cluster_centers : cluster center values
cluster_len : number of clusters
'''
# Initiate and fit the coordinates of pickup
kmeans = MiniBatchKMeans(n_clusters=increment, batch_size=10000,random_state=42).fit(coords)
# Predict the cluster number after fit the cluster
frame_with_durations_outliers_removed['pickup_cluster'] = kmeans.predict(frame_with_durations_outliers_removed[['pickup_latitude', 'pickup_longitude']])
# Store the cluster center values
cluster_centers = kmeans.cluster_centers_
# Store the number of clusters
cluster_len = len(cluster_centers)
return cluster_centers, cluster_len
def find_min_distance(cluster_centers, cluster_len):
nice_points = 0
wrong_points = 0
less2 = []
more2 = []
min_dist=1000
for i in range(0, cluster_len):
nice_points = 0
wrong_points = 0
for j in range(0, cluster_len):
# If both 'i' and 'j' have different cluster center value, we find the distance between two clusters value
# We know that cluster center value contain two part (X,Y) or (Lat., Long.)
if j!=i:
# "gpxpy.geo.haversine_distance" gives distance between two latitudes and longitudes in meters
distance = gpxpy.geo.haversine_distance(cluster_centers[i][0], cluster_centers[i][1],cluster_centers[j][0], cluster_centers[j][1])
# Convert it into miles
min_dist = min(min_dist,distance/(1.60934*1000))
# If distance (in miles) is less than 2 then increament nice point
# Otherwise increment wrong point
if (distance/(1.60934*1000)) <= 2:
nice_points +=1
else:
wrong_points += 1
# If both 'i' and 'j' have a same cluster center value then the distance will be 0
# Append the nice point value which tells that the two cluster center value is less than 2 miles
# Otherwise the wrong point value which tells that the two cluster center value is greater than 2 miles
less2.append(nice_points)
more2.append(wrong_points)
neighbours.append(less2)
print ("On choosing a cluster size of ",cluster_len,"\nAvg. Number of Clusters within the vicinity (i.e. intercluster-distance < 2):", np.ceil(sum(less2)/len(less2)), "\nAvg. Number of Clusters outside the vicinity (i.e. intercluster-distance > 2):", np.ceil(sum(more2)/len(more2)),"\nMin inter-cluster distance = ",min_dist,"\n---")
# Create Cluster
for increment in range(10, 100, 10):
cluster_centers, cluster_len = find_clusters(increment)
find_min_distance(cluster_centers, cluster_len)
Inference:¶
- The main objective was to find a optimal min. distance (Which roughly estimates to the radius of a cluster) between the clusters which we got was 40
In [62]:
# So we choose 40 clusters which contain minimum intercluster distance 0.5
# Instantiate and fit with 40 clusters using the KMeans
kmeans = MiniBatchKMeans(n_clusters=40, batch_size=10000,random_state=42).fit(coords)
# Store the pickup cluster value as per KMean predict value
frame_with_durations_outliers_removed['pickup_cluster'] = kmeans.predict(frame_with_durations_outliers_removed[['pickup_latitude', 'pickup_longitude']])
In [63]:
# Plot the cluster centers
cluster_centers = kmeans.cluster_centers_
cluster_len = len(cluster_centers)
map_osm = folium.Map(location=[40.734695, -73.990372], tiles='Stamen Toner')
for i in range(cluster_len):
folium.Marker(list((cluster_centers[i][0],cluster_centers[i][1])), popup=(str(cluster_centers[i][0])+str(cluster_centers[i][1]))).add_to(map_osm)
map_osm
Out[63]:
In [64]:
# Visualising the clusters on a map
def plot_clusters(frame):
# Define cluster long. bound value
city_long_border = (-74.03, -73.75)
# Define cluster lat. bound value
city_lat_border = (40.63, 40.85)
# Taking 100k as pickup cluster values
fig, ax = plt.subplots(ncols=1, nrows=1)
ax.scatter(frame.pickup_longitude.values[:100000], frame.pickup_latitude.values[:100000], s=10, lw=0,
c=frame.pickup_cluster.values[:100000], cmap='tab20', alpha=0.2)
ax.set_xlim(city_long_border)
ax.set_ylim(city_lat_border)
ax.set_xlabel('Longitude')
ax.set_ylabel('Latitude')
plt.show()
plot_clusters(frame_with_durations_outliers_removed)
Time Binning¶
In [75]:
# Refer:https://www.unixtimestamp.com/
# Unix TimeStamp : DateTime
# 1420070400 : 2015-01-01 00:00:00
# 1422748800 : 2015-02-01 00:00:00
# 1425168000 : 2015-03-01 00:00:00
# 1427846400 : 2015-04-01 00:00:00
# 1430438400 : 2015-05-01 00:00:00
# 1433116800 : 2015-06-01 00:00:00
# 1451606400 : 2016-01-01 00:00:00
# 1454284800 : 2016-02-01 00:00:00
# 1456790400 : 2016-03-01 00:00:00
# 1459468800 : 2016-04-01 00:00:00
# 1462060800 : 2016-05-01 00:00:00
# 1464739200 : 2016-06-01 00:00:00
def add_pickup_bins(frame,month,year):
unix_pickup_times=[i for i in frame['pickup_times'].values]
unix_times = [[1420070400,1422748800,1425168000,1427846400,1430438400,1433116800],\
[1451606400,1454284800,1456790400,1459468800,1462060800,1464739200]]
start_pickup_unix=unix_times[year-2015][month-1]
# convert_time_to_unix('2015-01-01 00:00:00') -> 1420050600
# from website (https://www.unixtimestamp.com/index.php) with same '2015-01-01 00:00:00' -> 1420070400
# There is differ among them. So we subtract both of them, we get -> -19800
# These are in seconds, to convert into minutes and also since we are doing time binning with 10 mins
# So, 10 mins means 600 seconds, so divide by 600, we get -> -33
# Now add 33 in order to get neutral to both timestamp
tenminutewise_binned_unix_pickup_times=[(int((i-start_pickup_unix)/600)+33) for i in unix_pickup_times]
frame['pickup_bins'] = np.array(tenminutewise_binned_unix_pickup_times)
return frame
In [76]:
# Making pickup bins
jan_2015_frame = add_pickup_bins(frame_with_durations_outliers_removed,1,2015)
In [79]:
# Grouping by pickup cluster and pickup bins
jan_2015_groupby = jan_2015_frame[['pickup_cluster','pickup_bins','trip_distance']].groupby(['pickup_cluster','pickup_bins']).count()
In [80]:
jan_2015_groupby.head()
Out[80]:
In [82]:
# Now we cleaned data and prepared data for the month 2015,
# now do the same operations for months Jan, Feb, March of 2016
# 1. get the dataframe which inlcudes only required colums
# 2. Adding Trip Times, Speed, Unix Timestamp of pickup_time
# 4. Remove the outliers- Trip duration, Speed, Trip Duration, Total Fare
# 5. add pickup_cluster to each data point
# 6. add pickup_bin (index of 10min interval to which that trip belongs to)
# 7. group by data, based on 'pickup_cluster' and 'pickup_bin'
# Data Preparation for the months of Jan,Feb and March 2016
def datapreparation(month,kmeans,month_no,year_no):
print('Data Preparation for {0} {1}'.format(month_no,year_no))
print ("Return with trip times..")
frame_with_durations = return_with_trip_times(month)
print ("Remove outliers..")
frame_with_durations_outliers_removed = remove_outliers(frame_with_durations)
print ("Estimating clusters..")
frame_with_durations_outliers_removed['pickup_cluster'] = kmeans.predict(frame_with_durations_outliers_removed[['pickup_latitude', 'pickup_longitude']])
print ("Final groupbying..")
final_updated_frame = add_pickup_bins(frame_with_durations_outliers_removed,month_no,year_no)
final_groupby_frame = final_updated_frame[['pickup_cluster','pickup_bins','trip_distance']].groupby(['pickup_cluster','pickup_bins']).count()
return final_updated_frame,final_groupby_frame
In [83]:
month_jan_2016 = dd.read_csv('yellow_tripdata_2016-01.csv')
month_feb_2016 = dd.read_csv('yellow_tripdata_2016-02.csv')
month_mar_2016 = dd.read_csv('yellow_tripdata_2016-03.csv')
In [84]:
jan_2016_frame,jan_2016_groupby = datapreparation(month_jan_2016,kmeans,1,2016)
feb_2016_frame,feb_2016_groupby = datapreparation(month_feb_2016,kmeans,2,2016)
mar_2016_frame,mar_2016_groupby = datapreparation(month_mar_2016,kmeans,3,2016)
Smoothing¶
In [88]:
# Gets the unique bins where pickup values are present for each each reigion
# for each cluster region, we will collect all the indices of 10min intervals in which the pickups are happened
# we got an observation that there are some pickup_bins that doesn't have any pickups
def return_unq_pickup_bins(frame):
values = []
for i in range(0,40):
new = frame[frame['pickup_cluster'] == i]
list_unq = list(set(new['pickup_bins']))
list_unq.sort()
values.append(list_unq)
return values
In [89]:
# for every month we get all indices of 10min intervals in which atleast one pickup got happened
# Jan
jan_2015_unique = return_unq_pickup_bins(jan_2015_frame)
jan_2016_unique = return_unq_pickup_bins(jan_2016_frame)
# Feb
feb_2016_unique = return_unq_pickup_bins(feb_2016_frame)
# March
mar_2016_unique = return_unq_pickup_bins(mar_2016_frame)
In [112]:
# Janurary has 31 days, each day is 24 hrs, and each hrs is 60 mins. Since we are taking 10mins intervals, we divide by 10
# i.e. 31*24*60/10
print('There are {} indices of 10mins inderval in Janurary'.format(31*24*60/10))
In [113]:
# For each cluster, number of 10min intervals with 0 pickups
# Subtract number of indices in each cluster from Total number of each ckuster in Janurary(4464)
for i in range(40):
print("for the ",i,"th cluster number of 10min intervals with zero pickups: ",4464 - len(set(jan_2015_unique[i])))
print('-'*60)
there are two ways to fill up these values
- Fill the missing value with 0's
- Fill the missing values with the avg values
- Case 1:(values missing at the start)
Ex1: \_ \_ \_ x =>ceil(x/4), ceil(x/4), ceil(x/4), ceil(x/4)
Ex2: \_ \_ x => ceil(x/3), ceil(x/3), ceil(x/3) - Case 2:(values missing in middle)
Ex1: x \_ \_ y => ceil((x+y)/4), ceil((x+y)/4), ceil((x+y)/4), ceil((x+y)/4)
Ex2: x \_ \_ \_ y => ceil((x+y)/5), ceil((x+y)/5), ceil((x+y)/5), ceil((x+y)/5), ceil((x+y)/5) - Case 3:(values missing at the end)
Ex1: x \_ \_ \_ => ceil(x/4), ceil(x/4), ceil(x/4), ceil(x/4)
Ex2: x \_ => ceil(x/2), ceil(x/2)
- Case 1:(values missing at the start)
In [123]:
# Fill 0 where there is no pickup in each and every cluster
def fill_missing(count_values,values):
smoothed_regions=[]
ind=0
# Loop of each cluster value
for r in range(0,40):
smoothed_bins=[]
# Total of indices 10 mins interval in Janurary
for i in range(4464):
# If values is present in the cluster. Then No effect of that value
if i in values[r]:
smoothed_bins.append(count_values[ind])
ind+=1
else:
# If value is not present in the cluster, then filled with 0
smoothed_bins.append(0)
smoothed_regions.extend(smoothed_bins)
return smoothed_regions
In [124]:
# Fill the avg value where there is no pickup in each and every cluster
def smoothing(count_values,values):
smoothed_regions=[] # stores list of final smoothed values of each reigion
ind=0
repeat=0
smoothed_value=0
for r in range(0,40):
smoothed_bins=[] #stores the final smoothed values
repeat=0
for i in range(4464):
if repeat!=0: # prevents iteration for a value which is already visited/resolved
repeat-=1
continue
if i in values[r]: #checks if the pickup-bin exists
smoothed_bins.append(count_values[ind]) # appends the value of the pickup bin if it exists
else:
if i!=0:
right_hand_limit=0
for j in range(i,4464):
if j not in values[r]: #searches for the left-limit or the pickup-bin value which has a pickup value
continue
else:
right_hand_limit=j
break
if right_hand_limit==0:
#Case 1: When we have the last/last few values are found to be missing,hence we have no right-limit here
smoothed_value=count_values[ind-1]*1.0/((4463-i)+2)*1.0
for j in range(i,4464):
smoothed_bins.append(math.ceil(smoothed_value))
smoothed_bins[i-1] = math.ceil(smoothed_value)
repeat=(4463-i)
ind-=1
else:
#Case 2: When we have the missing values between two known values
smoothed_value=(count_values[ind-1]+count_values[ind])*1.0/((right_hand_limit-i)+2)*1.0
for j in range(i,right_hand_limit+1):
smoothed_bins.append(math.ceil(smoothed_value))
smoothed_bins[i-1] = math.ceil(smoothed_value)
repeat=(right_hand_limit-i)
else:
#Case 3: When we have the first/first few values are found to be missing,hence we have no left-limit here
right_hand_limit=0
for j in range(i,4464):
if j not in values[r]:
continue
else:
right_hand_limit=j
break
smoothed_value=count_values[ind]*1.0/((right_hand_limit-i)+1)*1.0
for j in range(i,right_hand_limit+1):
smoothed_bins.append(math.ceil(smoothed_value))
repeat=(right_hand_limit-i)
ind+=1
smoothed_regions.extend(smoothed_bins)
return smoothed_regions
In [125]:
#Filling Missing values of Jan-2015 with 0
# here in jan_2015_groupby dataframe the trip_distance represents the number of pickups that are happened
jan_2015_fill = fill_missing(jan_2015_groupby['trip_distance'].values,jan_2015_unique)
#Smoothing Missing values of Jan-2015
jan_2015_smooth = smoothing(jan_2015_groupby['trip_distance'].values,jan_2015_unique)
In [126]:
# number of 10min indices for jan 2015= 24*31*60/10 = 4464
# number of 10min indices for jan 2016 = 24*31*60/10 = 4464
# number of 10min indices for feb 2016 = 24*29*60/10 = 4176
# number of 10min indices for march 2016 = 24*30*60/10 = 4320
# for each cluster we will have 4464 values, therefore 40*4464 = 178560 (length of the jan_2015_fill)
print("number of 10min intervals among all the clusters ",len(jan_2015_fill))
In [129]:
# Smoothing vs Filling
# sample plot that shows two variations of filling missing values
# we have taken the number of pickups for cluster region 33
plt.figure(figsize=(10,5))
plt.plot(jan_2015_fill[4464*33:4464*34-1], label="zero filled values")
plt.plot(jan_2015_smooth[4464*33:4464*34-1], label="filled with avg values")
plt.legend()
plt.show()
In [120]:
# Jan-2015 data is smoothed, Jan,Feb & March 2016 data missing values are filled with zero
jan_2015_smooth = smoothing(jan_2015_groupby['trip_distance'].values,jan_2015_unique)
jan_2016_smooth = fill_missing(jan_2016_groupby['trip_distance'].values,jan_2016_unique)
feb_2016_smooth = fill_missing(feb_2016_groupby['trip_distance'].values,feb_2016_unique)
mar_2016_smooth = fill_missing(mar_2016_groupby['trip_distance'].values,mar_2016_unique)
# Making list of all the values of pickup data in every bin for a period of 3 months and storing them region-wise
regions_cum = []
# a =[1,2,3]
# b = [2,3,4]
# a+b = [1, 2, 3, 2, 3, 4]
# number of 10min indices for jan 2015= 24*31*60/10 = 4464
# number of 10min indices for jan 2016 = 24*31*60/10 = 4464
# number of 10min indices for feb 2016 = 24*29*60/10 = 4176
# number of 10min indices for march 2016 = 24*31*60/10 = 4464
# regions_cum: it will contain 40 lists, each list will contain 4464+4176+4464 values which represents the number of pickups
# that are happened for three months in 2016 data
for i in range(0,40):
regions_cum.append(jan_2016_smooth[4464*i:4464*(i+1)]+feb_2016_smooth[4176*i:4176*(i+1)]+mar_2016_smooth[4464*i:4464*(i+1)])
# print(len(regions_cum))
# 40
# print(len(regions_cum[0]))
# 13104
Time series and Fourier Transforms¶
In [130]:
def uniqueish_color():
"""There're better ways to generate unique colors, but this isn't awful."""
return plt.cm.gist_ncar(np.random.random())
first_x = list(range(0,4464))
second_x = list(range(4464,8640))
third_x = list(range(8640,13104))
for i in range(40):
plt.figure(figsize=(10,4))
plt.plot(first_x,regions_cum[i][:4464], color='r', label='2016 Jan month data')
plt.plot(second_x,regions_cum[i][4464:8640], color='g', label='2016 feb month data')
plt.plot(third_x,regions_cum[i][8640:], color='b', label='2016 march month data')
plt.legend()
plt.show()
In [131]:
# getting peaks: https://blog.ytotech.com/2015/11/01/findpeaks-in-python/
# read more about fft function : https://docs.scipy.org/doc/numpy/reference/generated/numpy.fft.fft.html
Y = np.fft.fft(np.array(jan_2016_smooth)[0:4460])
# read more about the fftfreq: https://docs.scipy.org/doc/numpy/reference/generated/numpy.fft.fftfreq.html
freq = np.fft.fftfreq(4460, 1)
n = len(freq)
plt.figure()
plt.plot( freq[:int(n/2)], np.abs(Y)[:int(n/2)] )
plt.xlabel("Frequency")
plt.ylabel("Amplitude")
plt.show()
---¶
In [132]:
#Preparing the Dataframe only with x(i) values as jan-2015 data and y(i) values as jan-2016
# Given -> Jan 2015 Smoothing
# Prediction -> Jan 2016 Smoothing
# Ratios -> Prediction/Given
ratios_jan = pd.DataFrame()
ratios_jan['Given']=jan_2015_smooth
ratios_jan['Prediction']=jan_2016_smooth
ratios_jan['Ratios']=ratios_jan['Prediction']*1.0/ratios_jan['Given']*1.0
Modelling: Baseline Models¶
Now we get into modelling in order to forecast the pickup densities for the months of Jan, Feb and March of 2016 for which we are using multiple models with two variations
- Using Ratios of the 2016 data to the 2015 data i.e $\begin{align} R_{t} = P^{2016}_{t} / P^{2015}_{t} \end{align}$
- Using Previous known values of the 2016 data itself to predict the future values
Simple Moving Averages¶
The First Model used is the Moving Averages Model which uses the previous n values in order to predict the next value
Using Ratio Values - $\begin{align}R_{t} = ( R_{t-1} + R_{t-2} + R_{t-3} .... R_{t-n} )/n \end{align}$
In [138]:
(ratios_jan['Ratios'].values)
Out[138]:
In [173]:
def MA_R_Predictions(ratios,month):
predicted_ratio=(ratios['Ratios'].values)[0]
error=[]
predicted_values=[]
window_size=3
predicted_ratio_values=[]
# There are 40 clusters and each cluster contain 4464 indices of 10 mins intervals
for i in range(0,4464*40):
# if i equals 4464, that means we moving to the next cluster region
if i%4464==0:
predicted_ratio_values.append(0)
predicted_values.append(0)
error.append(0)
continue
# Initial ratio value R(t-1)
predicted_ratio_values.append(predicted_ratio)
# Add next predict value
# Calculate as R(t-1)*P_2015(t-1)
predicted_values.append(int(((ratios['Given'].values)[i])*predicted_ratio))
# Calculate error -> R(t)*P_2015(t) - P_2016(t)
error.append(abs((math.pow(int(((ratios['Given'].values)[i])*predicted_ratio)-(ratios['Prediction'].values)[i],1))))
if i+1>=window_size:
# Sum of three previous ratio (as window size = 3): R(t-3)+R(t-2)+R(t-1)/3 (as n=3)
predicted_ratio=sum((ratios['Ratios'].values)[(i+1)-window_size:(i+1)])/window_size
else:
# Sum of two previous ratio R(t-2)+R(t-1)/ 2 (as n=2)
predicted_ratio=sum((ratios['Ratios'].values)[0:(i+1)])/(i+1)
ratios['MA_R_Predicted'] = predicted_values
ratios['MA_R_Error'] = error
# MAPE -> Avg Error / Avg P_2016 or more likely |P_2015-P_2016|/P_2016
mape_err = (sum(error)/len(error))/(sum(ratios['Prediction'].values)/len(ratios['Prediction'].values))
# MSE -> Mean Square Error
mse_err = sum([e**2 for e in error])/len(error)
return ratios,mape_err,mse_err
For the above the Hyperparameter is the window-size (n) which is tuned manually and it is found that the window-size of 3 is optimal for getting the best results using Moving Averages using previous Ratio values therefore we get $\begin{align}R_{t} = ( R_{t-1} + R_{t-2} + R_{t-3})/3 \end{align}$
Next we use the Moving averages of the 2016 values itself to predict the future value using $\begin{align}P_{t} = ( P_{t-1} + P_{t-2} + P_{t-3} .... P_{t-n} )/n \end{align}$
In [174]:
def MA_P_Predictions(ratios,month):
predicted_value=(ratios['Prediction'].values)[0]
error=[]
predicted_values=[]
window_size=1
predicted_ratio_values=[]
for i in range(0,4464*40):
# Add prediction value P_2016(t-1)
predicted_values.append(predicted_value)
# Find error: P_2016(t-1)-P_2016(t)
error.append(abs((math.pow(predicted_value-(ratios['Prediction'].values)[i],1))))
if i+1>=window_size:
# Sum of three previous predicted P(t-3)+P(t-2)+P(t-1)/3 (as n=3 or more)
predicted_value=int(sum((ratios['Prediction'].values)[(i+1)-window_size:(i+1)])/window_size)
else:
# Sum of two previous predict P(t-2)+P(t-1)/ 2 (as n=2)
predicted_value=int(sum((ratios['Prediction'].values)[0:(i+1)])/(i+1))
ratios['MA_P_Predicted'] = predicted_values
ratios['MA_P_Error'] = error
# MAPE
mape_err = (sum(error)/len(error))/(sum(ratios['Prediction'].values)/len(ratios['Prediction'].values))
# MSE
mse_err = sum([e**2 for e in error])/len(error)
return ratios,mape_err,mse_err
For the above the Hyperparameter is the window-size (n) which is tuned manually and it is found that the window-size of 1 is optimal for getting the best results using Moving Averages using previous 2016 values therefore we get $\begin{align}P_{t} = P_{t-1} \end{align}$
Weighted Moving Averages¶
The Moving Avergaes Model used gave equal importance to all the values in the window used, but we know intuitively that the future is more likely to be similar to the latest values and less similar to the older values. Weighted Averages converts this analogy into a mathematical relationship giving the highest weight while computing the averages to the latest previous value and decreasing weights to the subsequent older ones
Weighted Moving Averages using Ratio Values - $\begin{align}R_{t} = ( N*R_{t-1} + (N-1)*R_{t-2} + (N-2)*R_{t-3} .... 1*R_{t-n} )/(N*(N+1)/2) \end{align}$
In [175]:
# Exactly same as simple mean but we add 'N' part only (in comment section) and rest of the section of code is same as
# simple mean.
def WA_R_Predictions(ratios,month):
predicted_ratio=(ratios['Ratios'].values)[0]
alpha=0.5
error=[]
predicted_values=[]
window_size=5
predicted_ratio_values=[]
for i in range(0,4464*40):
if i%4464==0:
predicted_ratio_values.append(0)
predicted_values.append(0)
error.append(0)
continue
predicted_ratio_values.append(predicted_ratio)
predicted_values.append(int(((ratios['Given'].values)[i])*predicted_ratio))
error.append(abs((math.pow(int(((ratios['Given'].values)[i])*predicted_ratio)-(ratios['Prediction'].values)[i],1))))
if i+1>=window_size:
sum_values=0
sum_of_coeff=0
# Here we are adding 'N' as windows size as per the formula
for j in range(window_size,0,-1):
sum_values += j*(ratios['Ratios'].values)[i-window_size+j]
sum_of_coeff+=j
predicted_ratio=sum_values/sum_of_coeff
else:
sum_values=0
sum_of_coeff=0
# Here we are adding 'N' as windows size as per the formula
for j in range(i+1,0,-1):
sum_values += j*(ratios['Ratios'].values)[j-1]
sum_of_coeff+=j
predicted_ratio=sum_values/sum_of_coeff
ratios['WA_R_Predicted'] = predicted_values
ratios['WA_R_Error'] = error
# MAPE
mape_err = (sum(error)/len(error))/(sum(ratios['Prediction'].values)/len(ratios['Prediction'].values))
# MSE
mse_err = sum([e**2 for e in error])/len(error)
return ratios,mape_err,mse_err
For the above the Hyperparameter is the window-size (n) which is tuned manually and it is found that the window-size of 5 is optimal for getting the best results using Weighted Moving Averages using previous Ratio values therefore we get $\begin{align} R_{t} = ( 5*R_{t-1} + 4*R_{t-2} + 3*R_{t-3} + 2*R_{t-4} + R_{t-5} )/15 \end{align}$
Weighted Moving Averages using Previous 2016 Values - $\begin{align}P_{t} = ( N*P_{t-1} + (N-1)*P_{t-2} + (N-2)*P_{t-3} .... 1*P_{t-n} )/(N*(N+1)/2) \end{align}$
In [176]:
# Exactly same as simple mean but we add 'N' part only (in comment section) and rest of the section of code is same as
# simple mean.
def WA_P_Predictions(ratios,month):
predicted_value=(ratios['Prediction'].values)[0]
error=[]
predicted_values=[]
window_size=2
for i in range(0,4464*40):
predicted_values.append(predicted_value)
error.append(abs((math.pow(predicted_value-(ratios['Prediction'].values)[i],1))))
if i+1>=window_size:
sum_values=0
sum_of_coeff=0
# Here we are adding 'N' as windows size as per the formula
for j in range(window_size,0,-1):
sum_values += j*(ratios['Prediction'].values)[i-window_size+j]
sum_of_coeff+=j
predicted_value=int(sum_values/sum_of_coeff)
else:
sum_values=0
sum_of_coeff=0
# Here we are adding 'N' as windows size as per the formula
for j in range(i+1,0,-1):
sum_values += j*(ratios['Prediction'].values)[j-1]
sum_of_coeff+=j
predicted_value=int(sum_values/sum_of_coeff)
ratios['WA_P_Predicted'] = predicted_values
ratios['WA_P_Error'] = error
# MAPE
mape_err = (sum(error)/len(error))/(sum(ratios['Prediction'].values)/len(ratios['Prediction'].values))
# MSE
mse_err = sum([e**2 for e in error])/len(error)
return ratios,mape_err,mse_err
For the above the Hyperparameter is the window-size (n) which is tuned manually and it is found that the window-size of 2 is optimal for getting the best results using Weighted Moving Averages using previous 2016 values therefore we get $\begin{align} P_{t} = ( 2*P_{t-1} + P_{t-2} )/3 \end{align}$
Exponential Weighted Moving Averages¶
https://en.wikipedia.org/wiki/Moving_average#Exponential_moving_average Through weighted averaged we have satisfied the analogy of giving higher weights to the latest value and decreasing weights to the subsequent ones but we still do not know which is the correct weighting scheme as there are infinetly many possibilities in which we can assign weights in a non-increasing order and tune the the hyperparameter window-size. To simplify this process we use Exponential Moving Averages which is a more logical way towards assigning weights and at the same time also using an optimal window-size.
In exponential moving averages we use a single hyperparameter alpha $\begin{align}(\alpha)\end{align}$ which is a value between 0 & 1 and based on the value of the hyperparameter alpha the weights and the window sizes are configured.
For eg. If $\begin{align}\alpha=0.9\end{align}$ then the number of days on which the value of the current iteration is based is~$\begin{align}1/(1-\alpha)=10\end{align}$ i.e. we consider values 10 days prior before we predict the value for the current iteration. Also the weights are assigned using $\begin{align}2/(N+1)=0.18\end{align}$ ,where N = number of prior values being considered, hence from this it is implied that the first or latest value is assigned a weight of 0.18 which keeps exponentially decreasing for the subsequent values.
$\begin{align}R^{'}_{t} = \alpha*R_{t-1} + (1-\alpha)*R^{'}_{t-1} \end{align}$
In [177]:
# Same as simple mean explaination code but one line of code change that is alpha( see comment section below)
def EA_R1_Predictions(ratios,month):
predicted_ratio=(ratios['Ratios'].values)[0]
alpha=0.6
error=[]
predicted_values=[]
predicted_ratio_values=[]
for i in range(0,4464*40):
if i%4464==0:
predicted_ratio_values.append(0)
predicted_values.append(0)
error.append(0)
continue
predicted_ratio_values.append(predicted_ratio)
predicted_values.append(int(((ratios['Given'].values)[i])*predicted_ratio))
error.append(abs((math.pow(int(((ratios['Given'].values)[i])*predicted_ratio)-(ratios['Prediction'].values)[i],1))))
# Here is the change with alpha parameter
predicted_ratio = (alpha*predicted_ratio) + (1-alpha)*((ratios['Ratios'].values)[i])
ratios['EA_R1_Predicted'] = predicted_values
ratios['EA_R1_Error'] = error
# MAPE
mape_err = (sum(error)/len(error))/(sum(ratios['Prediction'].values)/len(ratios['Prediction'].values))
# MSE
mse_err = sum([e**2 for e in error])/len(error)
return ratios,mape_err,mse_err
$\begin{align}P^{'}_{t} = \alpha*P_{t-1} + (1-\alpha)*P^{'}_{t-1} \end{align}$
In [178]:
# Same as simple mean explaination code but one line of code change that is alpha( see comment section below)
def EA_P1_Predictions(ratios,month):
predicted_value= (ratios['Prediction'].values)[0]
alpha=0.3
error=[]
predicted_values=[]
for i in range(0,4464*40):
if i%4464==0:
predicted_values.append(0)
error.append(0)
continue
predicted_values.append(predicted_value)
error.append(abs((math.pow(predicted_value-(ratios['Prediction'].values)[i],1))))
# Here is the change with alpha parameter
predicted_value =int((alpha*predicted_value) + (1-alpha)*((ratios['Prediction'].values)[i]))
ratios['EA_P1_Predicted'] = predicted_values
ratios['EA_P1_Error'] = error
# MAPE
mape_err = (sum(error)/len(error))/(sum(ratios['Prediction'].values)/len(ratios['Prediction'].values))
# MSE
mse_err = sum([e**2 for e in error])/len(error)
return ratios,mape_err,mse_err
In [179]:
mean_err=[0]*10
median_err=[0]*10
ratios_jan,mean_err[0],median_err[0]=MA_R_Predictions(ratios_jan,'jan')
ratios_jan,mean_err[1],median_err[1]=MA_P_Predictions(ratios_jan,'jan')
ratios_jan,mean_err[2],median_err[2]=WA_R_Predictions(ratios_jan,'jan')
ratios_jan,mean_err[3],median_err[3]=WA_P_Predictions(ratios_jan,'jan')
ratios_jan,mean_err[4],median_err[4]=EA_R1_Predictions(ratios_jan,'jan')
ratios_jan,mean_err[5],median_err[5]=EA_P1_Predictions(ratios_jan,'jan')
Comparison between baseline models¶
We have chosen our error metric for comparison between models as MAPE (Mean Absolute Percentage Error) so that we can know that on an average how good is our model with predictions and MSE (Mean Squared Error) is also used so that we have a clearer understanding as to how well our forecasting model performs with outliers so that we make sure that there is not much of a error margin between our prediction and the actual value
In [184]:
from prettytable import PrettyTable
x = PrettyTable()
x.field_names = ['Error Metric Matrix (Forecasting Methods)','MAPE','MSE']
x.add_row(['Moving Averages (Ratios)',mean_err[0],median_err[0]])
x.add_row(['Moving Averages (2016 Values)',mean_err[1],median_err[1]])
x.add_row(['-'*10,'-'*10,'-'*10])
x.add_row(['Weighted Moving Averages (Ratios)',mean_err[2],median_err[2]])
x.add_row(['Weighted Moving Averages (2016 Values)',mean_err[3],median_err[3]])
x.add_row(['-'*10,'-'*10,'-'*10])
x.add_row(['Exponential Moving Averages (Ratios)',mean_err[4],median_err[4]])
x.add_row(['Exponential Moving Averages (2016 Values)',mean_err[5],median_err[5]])
print(x)
Plese Note:- The above comparisons are made using Jan 2015 and Jan 2016 only
From the above matrix it is inferred that the best forecasting model for our prediction would be:- $\begin{align}P^{'}_{t} = \alpha*P_{t-1} + (1-\alpha)*P^{'}_{t-1} \end{align}$ i.e Exponential Moving Averages using 2016 Values
Regression Models¶
Prepare Data¶
In [325]:
# Preparing data to be split into train and test, The below prepares data in cumulative form which will be later split into test and train
# number of 10min indices for jan 2015= 24*31*60/10 = 4464
# number of 10min indices for jan 2016 = 24*31*60/10 = 4464
# number of 10min indices for feb 2016 = 24*29*60/10 = 4176
# number of 10min indices for march 2016 = 24*31*60/10 = 4464
# regions_cum: it will contain 40 lists, each list will contain 4464+4176+4464=13104 values which represents the
# number of pickups
# that are happened for three months in 2016 data
# print(len(regions_cum))
# 40
# print(len(regions_cum[0]))
# 12960
# We take number of pickups that are happened in last 5 10mins intervals
number_of_time_stamps = 5
regions_cum = []
# number of 10min indices for jan 2015= 24*31*60/10 = 4464
# number of 10min indices for jan 2016 = 24*31*60/10 = 4464
# number of 10min indices for feb 2016 = 24*29*60/10 = 4176
# number of 10min indices for march 2016 = 24*31*60/10 = 4464
# regions_cum: it will contain 40 lists, each list will contain 4464+4176+4464 values which represents the number of pickups
# that are happened for three months in 2016 data
for i in range(0,40):
regions_cum.append(jan_2016_smooth[4464*i:4464*(i+1)])
# output variable
# it is list of lists
# it will contain number of pickups 13104 for each cluster
output = []
# tsne_lat will contain 13104-5=13099 times lattitude of cluster center for every cluster
# Ex: [[cent_lat 13099times],[cent_lat 13099times], [cent_lat 13099times].... 40 lists]
# it is list of lists
tsne_lat = []
# tsne_lon will contain 13104-5=13099 times logitude of cluster center for every cluster
# Ex: [[cent_long 13099times],[cent_long 13099times], [cent_long 13099times].... 40 lists]
# it is list of lists
tsne_lon = []
# we will code each day
# sunday = 0, monday=1, tue = 2, wed=3, thur=4, fri=5,sat=6
# for every cluster we will be adding 13099 values, each value represent to which day of the week that pickup bin belongs to
# it is list of lists
tsne_weekday = []
# its an numbpy array, of shape (523960, 5)
# each row corresponds to an entry in out data
# for the first row we will have [f0,f1,f2,f3,f4] fi=number of pickups happened in i+1th 10min intravel(bin)
# the second row will have [f1,f2,f3,f4,f5]
# the third row will have [f2,f3,f4,f5,f6]
# and so on...
tsne_feature = []
tsne_feature = [0]*number_of_time_stamps
for i in range(0,40):
tsne_lat.append([kmeans.cluster_centers_[i][0]]*4459)
tsne_lon.append([kmeans.cluster_centers_[i][1]]*4459)
# jan 1st 2016 is thursday, so we start our day from 4: "(int(k/144))%7+4"
# our prediction start from 5th 10min interval since we need to have number of pickups that are happened in last 5 pickup bins
# tsne_weekday.append([int(((int(k/144))%7+4)%7) for k in range(5,4464+4176+4464)])
tsne_weekday.append([int(((int(k/144))%7+4)%7) for k in range(5,4464)])
# regions_cum is a list of lists [[x1,x2,x3..x13104], [x1,x2,x3..x13104], [x1,x2,x3..x13104], [x1,x2,x3..x13104], [x1,x2,x3..x13104], .. 40 lsits]
tsne_feature = np.vstack((tsne_feature, [regions_cum[i][r:r+number_of_time_stamps] for r in range(0,len(regions_cum[i])-number_of_time_stamps)]))
output.append(regions_cum[i][5:])
tsne_feature = tsne_feature[1:]
In [328]:
len(tsne_lat[0])*len(tsne_lat) == tsne_feature.shape[0] == len(tsne_weekday)*len(tsne_weekday[0]) == 40*4459 == len(output)*len(output[0])
Out[328]:
In [329]:
# Getting the predictions of exponential moving averages to be used as a feature in cumulative form
# upto now we computed 8 features for every data point that starts from 50th min of the day
# 1. cluster center lattitude
# 2. cluster center longitude
# 3. day of the week
# 4. f_t_1: number of pickups that are happened previous t-1th 10min intravel
# 5. f_t_2: number of pickups that are happened previous t-2th 10min intravel
# 6. f_t_3: number of pickups that are happened previous t-3th 10min intravel
# 7. f_t_4: number of pickups that are happened previous t-4th 10min intravel
# 8. f_t_5: number of pickups that are happened previous t-5th 10min intravel
# from the baseline models we said the exponential weighted moving avarage gives us the best error
# we will try to add the same exponential weighted moving avarage at t as a feature to our data
# exponential weighted moving avarage => p'(t) = alpha*p'(t-1) + (1-alpha)*P(t-1)
alpha=0.3
# it is a temporary array that store exponential weighted moving avarage for each 10min intravel,
# for each cluster it will get reset
# for every cluster it contains 13104 values
predicted_values=[]
# it is similar like tsne_lat
# it is list of lists
# predict_list is a list of lists [[x5,x6,x7..x13104], [x5,x6,x7..x13104], [x5,x6,x7..x13104], [x5,x6,x7..x13104], [x5,x6,x7..x13104], .. 40 lsits]
predict_list = []
tsne_flat_exp_avg = []
for r in range(0,40):
for i in range(0,4464):
if i==0:
predicted_value= regions_cum[r][0]
predicted_values.append(0)
continue
predicted_values.append(predicted_value)
predicted_value =int((alpha*predicted_value) + (1-alpha)*(regions_cum[r][i]))
predict_list.append(predicted_values[5:])
predicted_values=[]
In [330]:
amp = np.abs(np.fft.fft(regions_cum[0][:4464]))
freq = np.abs(np.fft.fftfreq(4464, 1))
n = len(freq)
amp = np.abs(amp)[:int(n/2)]
amp_index = np.argsort(-amp)[1:]
amp[amp_index[:5]]
Out[330]:
Top 5 FFT¶
In [380]:
amp_ = []
freq_ = []
for i in range(40):
amp = np.abs(np.fft.fft(regions_cum[i][:4464]))
freq = np.abs(np.fft.fftfreq(4464, 1))
n = len(freq)
amp = np.abs(amp)[:int(n/2)]
# Return indices of descending order of amplitude value
amp_index = np.argsort(-amp)[1:]
a = []
f = []
# Top 5 amplitudes and frequencies
a.append((amp[amp_index[:5]]))
# Corresponding amplitude we store frequency
f.append((freq[amp_index[:5]]))
# It will be same FFT for every each cluster
for k in range(4459):
amp_.append(a)
freq_.append(f)
Train-Test Split¶
Before we start predictions using the tree based regression models we take 3 months of 2016 pickup data and split it such that for every region we have 70% data in train and 30% in test, ordered date-wise for every region
In [333]:
# train, test split : 70% 30% split
# Before we start predictions using the tree based regression models we take Jan months of 2016 pickup data
# and split it such that for every region we have 70% data in train and 30% in test,
# ordered date-wise for every region
print("size of train data :", int(40*4459*0.7))
print("size of test data :", int(40*4459*0.3))
In [336]:
print('Size of train data in each cluster',int(4459*0.7))
print('Size of test data in each cluster',int(4459*0.3))
In [334]:
len(tsne_feature)
Out[334]:
In [337]:
# extracting first 9169 timestamp values i.e 70% of 13099 (total timestamps) for our training data
train_features = [tsne_feature[i*4459:(4459*i+3121)] for i in range(0,40)]
# temp = [0]*(12955 - 9068)
test_features = [tsne_feature[(4459*(i))+3121:4459*(i+1)] for i in range(0,40)]
In [339]:
print("Number of data clusters",len(train_features), "Number of data points in train data", len(train_features[0]), "Each data point contains", len(train_features[0][0]),"features")
print("Number of data clusters",len(train_features), "Number of data points in test data", len(test_features[0]), "Each data point contains", len(test_features[0][0]),"features")
In [341]:
# extracting first 9169 timestamp values i.e 70% of 13099 (total timestamps) for our training data
tsne_train_flat_lat = [i[:3121] for i in tsne_lat]
tsne_train_flat_lon = [i[:3121] for i in tsne_lon]
tsne_train_flat_weekday = [i[:3121] for i in tsne_weekday]
tsne_train_flat_output = [i[:3121] for i in output]
tsne_train_flat_exp_avg = [i[:3121] for i in predict_list]
In [407]:
train_freq = [freq_[i*4459:(4459*i+3121)] for i in range(40)]
train_amp = [amp_[i*4459:(4459*i+3121)] for i in range(40)]
In [342]:
# extracting the rest of the timestamp values i.e 30% of 12956 (total timestamps) for our test data
tsne_test_flat_lat = [i[3121:] for i in tsne_lat]
tsne_test_flat_lon = [i[3121:] for i in tsne_lon]
tsne_test_flat_weekday = [i[3121:] for i in tsne_weekday]
tsne_test_flat_output = [i[3121:] for i in output]
tsne_test_flat_exp_avg = [i[3121:] for i in predict_list]
In [408]:
test_freq = [freq_[(4459*i+3121):4459*(i+1)] for i in range(40)]
test_amp = [amp_[(4459*i+3121):4459*(i+1)] for i in range(40)]
In [417]:
np.array(train_freq[0]).shape, np.array(train_amp).shape
Out[417]:
In [424]:
train_new_features = []
test_new_features = []
train_fft = []
train_ampt = []
test_fft = []
test_ampt = []
for i in range(40):
train_new_features.extend(train_features[i])
train_fft.extend(np.array(train_freq[i]).reshape([3121,5]))
train_ampt.extend(np.array(train_amp[i]).reshape([3121,5]))
test_new_features.extend(test_features[i])
test_fft.extend(np.array(test_freq[i]).reshape([1338,5]))
test_ampt.extend(np.array(test_amp[i]).reshape([1338,5]))
In [425]:
np.array(train_new_features).shape,np.array(train_fft).shape,np.array(train_ampt).shape
Out[425]:
In [426]:
np.array(test_new_features).shape,np.array(test_fft).shape,np.array(test_ampt).shape
Out[426]:
Combine all feature using Hstack¶
In [428]:
# Hstack
import scipy
train_all_features = scipy.hstack((train_new_features,train_fft,train_ampt))
test_all_features = scipy.hstack((test_new_features,test_fft,test_ampt))
In [430]:
train_all_features.shape, test_all_features.shape
Out[430]:
In [431]:
columns = ['Latitude','Longitude','Weekday','Output','Exp. Avg','Freq_1','Freq_2','Freq_3','Freq_4','Freq_5',\
'Amp_1','Amp_2','Amp_3','Amp_4','Amp_5']
Train_DB = pd.DataFrame(data=train_all_features, columns=columns)
Test_DB = pd.DataFrame(data=test_all_features, columns=columns)
In [434]:
Train_DB.head()
Out[434]:
In [435]:
Test_DB.head()
Out[435]:
In [436]:
X_tr = Train_DB.drop('Output', axis=1).values
y_tr = Train_DB['Output'].values
In [439]:
X_ts = Test_DB.drop('Output', axis=1).values
y_ts = Test_DB['Output'].values
In [485]:
train_MAPE = []
train_MSE = []
test_MAPE = []
test_MSE = []
Using Linear Regression¶
In [486]:
# find more about LinearRegression function here http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html
# -------------------------
# default paramters
# sklearn.linear_model.LinearRegression(fit_intercept=True, normalize=False, copy_X=True, n_jobs=1)
# some of methods of LinearRegression()
# fit(X, y[, sample_weight]) Fit linear model.
# get_params([deep]) Get parameters for this estimator.
# predict(X) Predict using the linear model
# score(X, y[, sample_weight]) Returns the coefficient of determination R^2 of the prediction.
# set_params(**params) Set the parameters of this estimator.
# -----------------------
# video link: https://www.appliedaicourse.com/course/applied-ai-course-online/lessons/geometric-intuition-1-2-copy-8/
# -----------------------
from sklearn.linear_model import LinearRegression, SGDRegressor
from sklearn.model_selection import GridSearchCV
from sklearn.preprocessing import StandardScaler
scalar = StandardScaler()
X_tr_st = scalar.fit_transform(X_tr)
X_ts_st = scalar.transform(X_ts)
lr_reg=SGDRegressor(loss='squared_loss', random_state=1)
parameters = {'penalty':['l1','l2'],
'alpha':[10**-6, 10**-4, 10**-2, 10**0, 10**2, 10**4, 10**6]}
grid_clf = GridSearchCV(lr_reg,parameters,cv=3,scoring='neg_median_absolute_error',verbose=1)
grid_clf.fit(X_tr_st,y_tr)
Out[486]:
In [487]:
alpha = grid_clf.best_params_['alpha']
penalty = grid_clf.best_params_['penalty']
In [488]:
lr_reg=SGDRegressor(loss='squared_loss', alpha=alpha, penalty=penalty, random_state=1)
lr_reg.fit(X_tr_st,y_tr)
y_pred = lr_reg.predict(X_ts_st)
lr_test_predictions = [round(value) for value in y_pred]
y_pred = lr_reg.predict(X_tr_st)
lr_train_predictions = [round(value) for value in y_pred]
In [489]:
len(lr_train_predictions), len(y_tr)
Out[489]:
In [490]:
train_MAPE.append(mean_absolute_error(y_tr, lr_train_predictions)/ (sum(y_tr)/len(y_tr)))
train_MSE.append(mean_squared_error(y_tr, lr_train_predictions))
test_MAPE.append(mean_absolute_error(y_ts, lr_test_predictions)/ (sum(y_ts)/len(y_ts)))
test_MSE.append(mean_squared_error(y_ts, lr_test_predictions))
In [491]:
train_MAPE[0],train_MSE[0],test_MAPE[0],test_MSE[0]
Out[491]:
Using Random Forest Regressor¶
In [492]:
# Training a hyper-parameter tuned random forest regressor on our train data
# find more about LinearRegression function here http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html
# -------------------------
# default paramters
# sklearn.ensemble.RandomForestRegressor(n_estimators=10, criterion=’mse’, max_depth=None, min_samples_split=2,
# min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features=’auto’, max_leaf_nodes=None, min_impurity_decrease=0.0,
# min_impurity_split=None, bootstrap=True, oob_score=False, n_jobs=1, random_state=None, verbose=0, warm_start=False)
# some of methods of RandomForestRegressor()
# apply(X) Apply trees in the forest to X, return leaf indices.
# decision_path(X) Return the decision path in the forest
# fit(X, y[, sample_weight]) Build a forest of trees from the training set (X, y).
# get_params([deep]) Get parameters for this estimator.
# predict(X) Predict regression target for X.
# score(X, y[, sample_weight]) Returns the coefficient of determination R^2 of the prediction.
# -----------------------
# video link1: https://www.appliedaicourse.com/course/applied-ai-course-online/lessons/regression-using-decision-trees-2/
# video link2: https://www.appliedaicourse.com/course/applied-ai-course-online/lessons/what-are-ensembles/
# -----------------------
from sklearn.model_selection import RandomizedSearchCV
regr1 = RandomForestRegressor(max_features='sqrt',n_jobs=-1, random_state=1)
parameters = {'min_samples_leaf':[2,3,4],
'min_samples_split':[3,4,5],
'n_estimators':[10,20,40,70,100]}
rand_clf = RandomizedSearchCV(regr1,parameters,cv=3,verbose=1, scoring='neg_median_absolute_error')
rand_clf.fit(X_tr,y_tr)
Out[492]:
In [493]:
rand_clf.best_params_
Out[493]:
In [494]:
regr1 = RandomForestRegressor(max_features='sqrt',n_jobs=-1, n_estimators=100, min_samples_leaf=4, min_samples_split=4, random_state=1)
regr1.fit(X_tr,y_tr)
y_pred = regr1.predict(X_ts)
rndf_test_predictions = [round(value) for value in y_pred]
y_pred = regr1.predict(X_tr)
rndf_train_predictions = [round(value) for value in y_pred]
In [495]:
train_MAPE.append(mean_absolute_error(y_tr, rndf_train_predictions)/ (sum(y_tr)/len(y_tr)))
train_MSE.append(mean_squared_error(y_tr, rndf_train_predictions))
test_MAPE.append(mean_absolute_error(y_ts, rndf_test_predictions)/ (sum(y_ts)/len(y_ts)))
test_MSE.append(mean_squared_error(y_ts, rndf_test_predictions))
In [496]:
#feature importances based on analysis using random forest
print (Train_DB.drop(['Output'],axis=1).columns)
print (regr1.feature_importances_)
In [497]:
train_MAPE[1],train_MSE[1],test_MAPE[1],test_MSE[1]
Out[497]:
Using XgBoost Regressor¶
In [498]:
# Training a hyper-parameter tuned Xg-Boost regressor on our train data
# find more about XGBRegressor function here http://xgboost.readthedocs.io/en/latest/python/python_api.html?#module-xgboost.sklearn
# -------------------------
# default paramters
# xgboost.XGBRegressor(max_depth=3, learning_rate=0.1, n_estimators=100, silent=True, objective='reg:linear',
# booster='gbtree', n_jobs=1, nthread=None, gamma=0, min_child_weight=1, max_delta_step=0, subsample=1, colsample_bytree=1,
# colsample_bylevel=1, reg_alpha=0, reg_lambda=1, scale_pos_weight=1, base_score=0.5, random_state=0, seed=None,
# missing=None, **kwargs)
# some of methods of RandomForestRegressor()
# fit(X, y, sample_weight=None, eval_set=None, eval_metric=None, early_stopping_rounds=None, verbose=True, xgb_model=None)
# get_params([deep]) Get parameters for this estimator.
# predict(data, output_margin=False, ntree_limit=0) : Predict with data. NOTE: This function is not thread safe.
# get_score(importance_type='weight') -> get the feature importance
# -----------------------
# video link1: https://www.appliedaicourse.com/course/applied-ai-course-online/lessons/regression-using-decision-trees-2/
# video link2: https://www.appliedaicourse.com/course/applied-ai-course-online/lessons/what-are-ensembles/
# -----------------------
x_model = xgb.XGBRegressor(colsample_bytree=0.8,nthread=4,random_state=1)
parameters = {'learning_rate':np.random.uniform(0.0001,0.1,size=5),
'n_estimators':[10,20,50,100,500,1000],
'max_depth':[2,3,4,5],
'min_child_weight':[3,4,5],
'subsample':[0.5,0.6,0.7,0.8],
'reg_alpha':[50,100,150,200],
'reg_lambda':[50,100,150,200]}
rand_clf = RandomizedSearchCV(x_model,parameters,cv=3,verbose=1,scoring='neg_median_absolute_error')
rand_clf.fit(X_tr,y_tr)
Out[498]:
In [499]:
rand_clf.best_params_
Out[499]:
In [500]:
x_model = xgb.XGBRegressor(subsample=0.7,reg_lambda=50,reg_alpha=150,n_estimators=100,
min_child_weight=5, max_depth=4, learning_rate=0.03892878525507715,
colsample_bytree=0.8,nthread=4,random_state=1)
x_model.fit(X_tr,y_tr)
y_pred = x_model.predict(X_ts)
xgb_test_predictions = [round(value) for value in y_pred]
y_pred = x_model.predict(X_tr)
xgb_train_predictions = [round(value) for value in y_pred]
In [501]:
train_MAPE.append(mean_absolute_error(y_tr, xgb_train_predictions)/ (sum(y_tr)/len(y_tr)))
train_MSE.append(mean_squared_error(y_tr, xgb_train_predictions))
test_MAPE.append(mean_absolute_error(y_ts, xgb_test_predictions)/ (sum(y_ts)/len(y_ts)))
test_MSE.append(mean_squared_error(y_ts, xgb_test_predictions))
In [502]:
train_MAPE[2],train_MSE[2],test_MAPE[2],test_MSE[2]
Out[502]:
Calculating the error metric values for various models¶
In [503]:
from prettytable import PrettyTable
x = PrettyTable()
x.field_names = ['Model','Train MAPE','Train MSE','Test MAPE','Test MSE']
x.add_row(['Linear Regression',train_MAPE[0]*100,train_MSE[0],test_MAPE[0]*100,test_MSE[0]])
x.add_row(['RF Regression',train_MAPE[1]*100,train_MSE[1],test_MAPE[1]*100,test_MSE[1]])
x.add_row(['XGBoost Regression',train_MAPE[2]*100,train_MSE[2],test_MAPE[2]*100,test_MSE[2]])
print(x)
Conclusion¶
- Data cleaning by removing outliers:
- pickup and dropoff latitude and longtitude value
- trip duration
- distance
- speed
- Data Preparation:
- Clustering using KMeans Algo
- Time Binning with 10 mins interval
- Smoothing
- Time Fourier Series
- Perform Baseline Model (Both Ratios and Predictions)
- Simple Moving Average
- Weighted Moving Average
- Exponential Weighted Moving Average
- Compare the baseline model
- Perform ML Regression Model
- Linear Regression
- Random Forest Regression
- XGBoost Regression
Final conclusion: Linear Regression perform better with Train MAPE: 11.221536412055098 and Test MAPE: 11.274097216729807
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